Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include<cstdio>
#include<algorithm>
using namespace std;
#define MAXN 200010
int p[MAXN],n,T[MAXN],f[MAXN];
bool check(int a,int b,int c)
{
	return (a<b&&b<c)||(b<c&&c<a)||(c<a&&a<b);
}
int main()
{
	int x;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&x);
		p[x]=i;
	}
	for(int i=n-1;i;i--)
		if(T[i+1]==0)
		{
			if(p[i]>p[i+1])
				T[i]=1,f[i]=i+1;
		}
		else
		{
			if(check(p[f[i+1]],p[i],p[i+1]))
				T[i]=T[i+1],f[i]=f[i+1];
			else T[i]=T[i+1]+1,f[i]=i+1;
		}
	printf("%d\n",T[1]);
}